Mathematical model and method of searching for a local extremum for the non-convex oriented polygons allocation problem

Stoyan, Yu. G.; Novozhilova, M. V.; Kartashov, A.V.

doi:10.1016/0377-2217(95)00038-0

Cited by 45 publications

(18 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…In particular Stoyan et al (1996Stoyan et al ( , 2002Stoyan et al ( , 2004 defined the -functions of two-dimensional regular and irregular shape objects. Scheithauer et al (2005) defined the -functions for pair of three-dimensional regular shape objects.…”

Section: Literature Reviewmentioning

confidence: 99%

A fast heuristic for a three-dimensional non-convex domain loading problem

et al. 2010

View full text Add to dashboard Cite

In this paper we tackle a three-dimensional non-convex domain loading problem. We have to efficiently load identical small boxes into a highly irregular non-convex domain. The boxes to be loaded have a particular shape. If d is the length of the smallest edge of the box, its dimensions are d × nd × md, n ≤ m, with n and m integer values. This loading problem arises from an industrial design problem where it is necessary to obtain good solutions with very low computation time. We propose a fast heuristic based on an approximate representation of the non-convex domain in terms of cubes of dimension d and on the decomposition of the whole problem in several two-dimensional subproblems related to ‘planes’ of height d. The proposed heuristic shows good performances in terms of quality of solution and computation times. The results on several real test cases, coming from the industrial application, are shown

show abstract

Section: Literature Reviewmentioning

confidence: 99%

A fast heuristic for a three-dimensional non-convex domain loading problem

et al. 2010

View full text Add to dashboard Cite

show abstract

“…Assume that the object set is given by (1), and allocation order is given by (5). According to this order, the grouping algorithm makes object groups using the same scan-field method described above, except that the scan-field method is limited to a one-line scan (y is fixed to zero and Step 3 is not repeated).…”

Section: Grouping Proceduresmentioning

confidence: 99%

“…The objects are allocated on a sheet such that waste is minimized. Such a problem arises in many industrial fields, such as the textile industry and the sheet metal industry [5,6]. This so-called nesting problem is NP-complete [7], hence no theoretically efficient algorithm seems to exist.…”

mentioning

confidence: 99%

Solution for textile nesting problems using adaptive meta-heuristics and grouping

Takahara

Kusumoto

Miyamoto

2003

Soft Computing - A Fusion of Foundations, Methodologies and App

View full text Add to dashboard Cite

An optimal packing problem of non-convex polygons on a sheet is considered and applied to a textile nesting problem. We propose a procedure of grouping objects and adaptive meta-heuristics. The grouping procedure classifies objects into groups which are then allocated on the sheet using adaptive meta-heuristics. As a result, effectiveness of the meta-heuristics is improved. The performance of the proposed method is compared with other meta-heuristics using simulation experiments. The result shows that the present method is superior to cases where adaptive meta-heuristics without grouping are used. IntroductionWith the remarkable increase of computer capability, new research in optimization algorithms of meta-heuristics is becoming more popular and much research has been done on real applications. Three major methodologies in metaheuristics are simulated annealing [1], genetic algorithms [2], and tabu search [3,4]. They should be remarked upon for their practical usefulness as well as fundamental ideas. Unlike the traditional methods of optimization on the basis of rigorous mathematics, they use heuristics whereby obtained solutions are, in general, not strictly optimal. However, the methodologies are simple, flexible, applicable to many real complex problems, and produce practical solutions.A notable feature of these methodologies is that they are based on different fundamental paradigms. Simulated annealing is based on a physical paradigm while genetic algorithms are based upon a biological paradigm. We can remark that a human paradigm exists under the tabu search, since human logic such as taboo is used, and moreover strategic search is used in contrast to a blind search in simulated annealing and genetic algorithms.We enhance the human features in the algorithms proposed in this paper. The proposed algorithms have adaptation mechanisms whereby search effectiveness is improved. These adaptation mechanisms use human logic and memories. By using such human mechanisms, the whole system becomes more human-oriented. We call these mechanisms adaptive meta-heuristics which have a number of options: adaptive local search, adaptive simulated annealing, and adaptive tabu search.The aim of the present paper is not to propose a general methodology. Rather, our purpose is to provide practical solutions for the real-world problem of the optimal allocation of irregular objects. The objects are allocated on a sheet such that waste is minimized. Such a problem arises in many industrial fields, such as the textile industry and the sheet metal industry [5,6]. This so-called nesting problem is NP-complete [7], hence no theoretically efficient algorithm seems to exist. However, there have been several approaches, such as linear programming [8], expert system [9], heuristic procedure [10], and metaheuristic approach [11,12]. The meta-heuristic approach has shown good performance, but in order to tackle problems of complicated shapes, further improvement to the algorithm is required.The present method consists of two stages. In the f...

show abstract

“…A mixed-integer programming model to represent the irregular strip packing problem can be derived from the compaction models that were used in literature as part of heuristic methods (Li and Milenkovic, 1995;Stoyan et al, 1996;Bennell and Dowsland, 2001;Gomes and Oliveira, 2006 …”

Section: A Linear Model Based On Compaction Strategiesmentioning

confidence: 99%

Nesting problems

Cherri¹

View full text Add to dashboard Cite

Mathematical model and method of searching for a local extremum for the non-convex oriented polygons allocation problem

Cited by 45 publications

References 4 publications

A fast heuristic for a three-dimensional non-convex domain loading problem

A fast heuristic for a three-dimensional non-convex domain loading problem

Solution for textile nesting problems using adaptive meta-heuristics and grouping

Nesting problems

Contact Info

Product

Resources

About